posted 01. September 2006 01:30                   

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Chris wrote:

Can't really agree – I am sure specification can be put on an objective footing.

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Dirac's mathematical manipulations and physical speculations would have remained just that except for two facts: (1) In 1932 Carl Anderson experimentally confirmed the existence of the positron. (2) In the nineteenth century mathematicians had already constructed the "number-like" objects that Dirac needed to factor the Klein-Gordon equation. They are known today collectively as the Clifford algebra, and Dirac had to reinvent it to get a relativistic equation for the electron.

Where is the philosophical problem for naturalism in examples like this (and Steiner makes clear that such examples are wide spread throughout mathematics in its application to physics)? The problem is that mathematics is a thoroughly human enterprise. Nature may condition us to see patterns that are readily perceived--that, as it were, ride on the surface structure of nature. At the same time, nature should be indifferent to human idiosyncrasies. Thus, the problem for naturalism posed by Dirac's reinvention of the Clifford algebra and subsequent discovery of antimatter is that it occurred entirely through the manipulation of humanly constructed notations, and with attention not to physical reality but to human convenience.

Equations that are factorable are much easier for us to deal with than those that are not. Factorability, however, has no physical significance. A world indifferent to us has no stake in rendering itself intelligible to us by making the equations that describe it factorable through some mathematical device (like the Clifford algebra). And yet precisely such idiosyncratic manipulations of humanly constructed notations result in genuine and previously unsuspected physical insights.

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posted 01. September 2006 21:16                   

Hi Sal,
Thanks for welcoming me back.

I have taken this quote of yours from your second post of this thread. I consider it an important (and on topic) question because by the end of it your face was blue and your eyes were bulging way out of your head .

Salvador Cordova -- posted 17. May 2005 22:49

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The 2nd law is a measure of the deterioration of orderliness and increase in K-complexity, Ironically in this case, an increase in K-complexity is a decrease in specified complexity.

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You also suggest in that post that a diagram might help. The following is my diagram of Information Density Continuum based upon my own model.



The second law typically starts at "Order" in the middle of the diagram, order that becomes more and more fractured ({m}K-complex) over time. This fracturing undermines any CSI in the system. DNA, in this model is a form of nanotechnology (specified). A typical gas or macroscopic entity does not contain nanotechnologies nor the attendant high info-density.

"Mock-information" is the "information" contained in a random coin toss or the "patterns" that individual photons make in the double slit experiment. While it is possible to draw K-complex lines from photon hit to photon hit to make patterns, the only real pattern is the composite statistical interference pattern. Randomness lacks any pattern IMO.

posted 03. September 2006 23:24                   

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An example of k-simple CSI is:

[pi> = 11001001000011111101101010100010001000010110100011..

The first 50 bits of pi=3.14 etc as derived by a simple computer algorithm (5th miracle, Davies, p117):

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posted 04. September 2006 02:56                   

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There is another, somewhat philosophical school of thought (due primarily to Bohm and Broglie) which holds that the impossibility of QM to predict with certainty the outcome of a given measurement on an individual system stems from one’s inability to know the exact values of certain hidden variables relating to the system. In this description, the wavefunction is viewed as a mathematical object that contains all the information one possesses regarding an incompletely known system.

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I tend to agree - the idea that what we actually observe can be explained in terms of lack of information - epistemic randomness (rather than ontic randomness).
Phillip Engle points out in his excellent book , tha Bohm also created an expansive interpretation of QM which is much more of a comprehensive philosophy in which the implicate order of the cosmos is both higher-dimensional and holographic in nature. (In a holographic plate, an imperfect three-dimensional image of the whole exists within each part of the plate, as well as each part of the plate existing within the whole ) The following is a quotation from Bohm's book:

What might interest you is that Bohm also contributed to neuropsychology: Quoting Engle

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It seems likely, for example, that the human brain is some way physically contains some kind of imperfect structural correspondence with the larger physical universe which it both tries to represent and which, in turn, encompasses it as a physical part

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posted 05. September 2006 11:14                   

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Pi = 3.14.........................................................................587......
The "3.14" contains the "lions share" of the information about pi. The later sequence "..587.." is probably sub-plankian and informationally worthless. Pi is subsequently not CSI as far as I can tell.

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Boy, I had to go along way to find that 587 – it starts in the 33rd decimal place!
Pi=3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 724 587

Well I understand and feel what you are saying about the 3.14 – and why we feel this is the “Lions share” is certainly counterintuitive - more on this below. However I'd like to persuade you that the 50 bit pi string is CSI.

COMPLEX : The complexity part of Pi string is certainly not in doubt - It is determined by the complexity (or Shannon entropy = - Log2(Prob of this string happening by chance). So that the string :
[pi> = 11001001000011111101101010100010001000010110100011..
has 50 bits of Shannon entropy. If I can be forgiven for taking the UCB (Universal Complexity Bound) as 50 bits (rather than 500bits) then this string is to be labelled "complex"
SPECIFIED The Pi string is certainly specified – Why?, because the 50 bit sequence is non-random, and from the previous posts we have seen that any complex string that is non-random must be CSI . Why is the string non-random? Because it results from an algorithm (of relatively low complexity) that is in itself completely beyond the reach of chance. In short we have within our Pi string the outworkings of a detachable pattern (the algorithm).
I made this diagram to aid myself understand Chaitin, Kolmogorov, Solomonoff complexity – it is taken from Bill Dembski’s No Free Lunch (p61). I include it since it helped me and may be of use to you and others here.

Summarizing - a computer input register (I/P) has input string [u> which is say a Fortran program plus any input data. [u> executes and in doing so produces in deterministic fashion O/P string [v>=phi.[u>. Define scalar function f([v>) as the length l of the shortest program (algorithm) [u> that gives [v>. [u> is now part of an extremal set (Tsub(delta) having 2^delta members) for which inclusion in will not occur by chance. [The chance is ~2^(delta+1-N), and since N>>delta (N can be made as large as we wish) this will fall below the UPB]
This website gives many algorithms for Pi, all of which require continued iterations for increased accuracy – but all of which could be written into a simple “do-loop” comprising a few lines of code such as:

For n=1 to nmax (nmax arbitrarily large)
Calculate X(n)
Pi=Pi+X(n)

LIONS SHARE PROBLEM. According to the definition of Information one might write
Info=-log2(Probability of by chance falling within a standard deviation delta(Pi) of the true value of Pi = -log2 (delta(Pi)/2*Pi).
This will necessarily increase as the accuracy of Pi gets higher. I.E. the number of bits of data needed to describe what Pi is gets larger - this is understandable. But as you point out it is counterintuitive. What you want is the most significant bits to count as "primary information" on the value of Pi. Is there anyone out there who knows how to deal with this? Chris

[ 05. September 2006, 21:38: Message edited by: Christopher D. Beling ]

posted 05. September 2006 15:07                    

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The complexity part of Pi string is certainly not in doubt

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It is determined by the complexity (or Shannon entropy = - Log2(Prob of this string happening by chance).

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posted 05. September 2006 18:14                    

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I am interested - as to whether you see your “contextual= found elsewhere” condition as a necessary condition for CSI or a sufficient condition?

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posted 06. September 2006 21:40                   

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Dembski defines "chance" to include all natural processes.

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To sum up, contemporary science allows a principled distinction between necessity and chance, but repudiates design

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Another concern is that the filter will assign to design regular objects like the star-shaped ice crystals that form on a cold window. This criticism fails because such shapes form as a matter of physical necessity simply in virtue of the properties of water (the filter will therefore assign the crystals to necessity and not to design)

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Since pi can be measured with high precision from natural phenomena, it seems that P(T|H), where H includes all natural processes, is high

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namely that the digits (or bits) were randomly drawn from a uniform distribution.

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e.g. the number 0.0000... is also complex.

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Specifically, there must be both conceptual (i.e. identified by an agent) and physical instances of the pattern.

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posted 07. September 2006 14:03                    

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Dembski also includes "necessity" not just "chance".

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Which phenomenon are you talking about? – I am eager to know as I can think of none. Even when the planets go around the Sun they do not do so in perfect circles. But say a perfect circle were found – it will not automatically dump the value of pi into some DNA polymer or a computer register -i.e produce the pi string in question.

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I think probabilities are uniform being a-priori probabilities: - which you may not like. Could such probabilities (i.e. 0.5 for 0, 0.5 for 1) be definitional as regards a complexity measure?

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If there are 500 of those 0’s then surely that number IS complex. i.e. it is undifferentiated from other 500 bit strings in that it has the probability of 2 E-150 of occurring by chance (which it cannot do - being below the UPB). Your string is, however, special because it could have occurred either through necessity (regularity) or design

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I do think, however, one has to distinguish between humanly made CSI (i.e. credit card numbers) and naturally occurring CSI.. It is perhaps only in naturally occurring CSI that more objectivity in specification might be found - i.e. in the concept and definition of life.

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posted 07. September 2006 22:11                    

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It seems to me that examples like credit card numbers aren't even necessarily human-made. If they aren't generated randomly, it seems that they could be. So if they have CSI, then CSI can apparently be generated randomly.

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posted 08. September 2006 12:30                    

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The sixteen-digit number on your VISA card is an example of CSI. The complexity of this number ensures that a would-be thief cannot randomly pick a number and have it turn out to be a valid VISA number. What's more, the specification of this number ensures that it is your number, and not anyone else's. Even your phone number constitutes CSI. As with a VISA number, the complexity ensures that this number won't be dialed randomly (at least not too often), and the specification ensures that this number is yours and yours only. All the numbers on our bills, credit slips and purchase orders represent CSI. CSI makes the world go round.

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